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  4. Six boys and six girls are sitting in a row. The probability that all 6 girls sit together, is

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Q. Six boys and six girls are sitting in a row. The probability that all 6 girls sit together, is

Rajasthan PETRajasthan PET 2004

Solution:

Probability of sitting all girls together
$ =\frac{(6+1)!6!}{12!} $
$ =\frac{7!6!}{12.11.10.9.8.7!} $
$ =\frac{1.2.3.4.5.6}{12.11.10.9.8} $
$ =\frac{1}{132} $